Constructed as a series of vaudeville turns, “Chicago’’ tells the story of a nobody who dreams of being a somebody, and whose stardom-at-any-price ethos, coupled with her delusions of grandeur, would make her a perfect fit for our reality TV age of pseudo-celebrity. But whereas reality TV just kills time (and brain cells), Roxie commits actual murder: She shoots her lover when he tries to walk out on her.

Former supermodel Christie Brinkley, who plays Roxie in the touring production of “Chicago’’ that has arrived at the Citi Performing Arts Center Wang Theatre, has known fame for more than 30 years. But Brinkley is relatively new to musical theater — a fact that is unfortunately all too evident in her performance.

It’s never helpful when a musical has to struggle against the vocal limitations of its headliner. The same thing happened on Broadway with Daniel Rad­cliffe in “How to Succeed in Business Without Really Trying’’ and in the touring production of “La Cage Aux Folles,’’ starring George Hamilton, that came to Boston last year.

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Brinkley is by no means as excruciating to watch or listen to as Hamilton was, but her deficiencies as a singer are apparent from her very first number, “Funny Honey,’’ in which Roxie, from atop a ladder, pays sardonic homage to her chump of a husband. Similarly lackluster are her later renditions of “Roxie,’’ a potential showstopper if done right, and “Me and My Baby.’’ Brinkley does prove an adequate hoofer, and she is never less than game, but her Roxie is largely devoid of sizzle. And for “Chicago’’ to really work, Roxie has to sizzle and burn: with twisted ambition, with feral cunning, with desperation. We feel little of that in Brinkley’s performance.

Consequently, as with “How to Succeed’’ and “La Cage,’’ an audience member ends up looking forward to those moments when the pros will take over.

In this “Chicago,’’ that task falls to, among others, Amra-Faye Wright, who excels as Velma Kelly. Velma’s own crime of passion made her the toast of the town until Roxie came along, and Wright gives an amusing edge of spite to Velma, who is none too happy about being ignored by the tabloids, embodied by a reporter named Mary Sunshine (D. Micciche).

Also a substantial asset is John O’Hurley, who portrays Billy Flynn, defense attorney and spinmeister extraordinaire, with a mercenary glint in his eye, a swagger in his step, and that distinctive voice so familiar to “Seinfeld’’ fans. To Billy, the justice system is just another branch of showbiz, a notion made plain in “Razzle Dazzle,’’ as the lawyer elaborates on his methods of bamboozlement while the ensemble dances sinuously around him and sequins fall like snowflakes.

As Amos Hart, Roxie’s husband, Ron Orbach is overly maudlin, but Kecia Lewis-Evans delivers a solid performance as Matron “Mama’’ Morton, who runs the jail where Roxie and Velma are imprisoned. It is Mama who says of Chicago: “In this town, murder’s a form of entertainment.’’

For a show with such an astringent worldview, “Chicago’’ has proven remarkably popular. Americans apparently don’t mind looking in this particular mirror. “Chicago’’ premiered in 1975, directed and choreographed by the legendary Bob Fosse, who also collaborated on the book with Fred Ebb. Revived in 1996 under the direction of Walter Bobbie, with choreography “in the style of Bob Fosse’’ by Ann Reinking, “Chicago’’ went on to become one of the longest running shows in the history of Broadway, where it’s still playing.

The production at the Wang Theatre is a re-creation of the revival, and is directed by Scott Faris, with choreography by Gary Chryst. Fosse would be pleased by the dancing, which still carries his trademarks: It is carnality in motion, abounding in convulsive wriggling, pelvic thrusts, popped shoulders, splayed fingers, bowler hats hoisted on high.

The built-in strength of Kander and Ebb’s score is a plus, of course. Any chance to marinate in their jaunty cynicism is welcome, and “Chicago’’ offers a tangy slice early on with “Cell Block Tango,’’ in which Velma and a host of other murderesses, seated in chairs facing the audience, take turns spelling out just how and why they dispatched the nettlesome men in their lives, punctuating it with the defiant refrain: “He had it comin’/He had it comin’/He only had himself to blame.’’

It’s a juicy number, and it’s not the only one. Still, this “Chicago’’ is seldom truly electrifying.

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